Solve for $x$ and $y$ using elimination. ${-3x+4y = -20}$ ${2x-3y = 13}$
Explanation: We can eliminate $y$ by adding the equations together when the $y$ coefficients have opposite signs. Multiply the top equation by $3$ and the bottom equation by $4$ ${-9x+12y = -60}$ $8x-12y = 52$ Add the top and bottom equations together. $-x = -8$ $\dfrac{-x}{{-1}} = \dfrac{-8}{{-1}}$ ${x = 8}$ Now that you know ${x = 8}$ , plug it back into $\thinspace {-3x+4y = -20}\thinspace$ to find $y$ ${-3}{(8)}{ + 4y = -20}$ $-24+4y = -20$ $-24{+24} + 4y = -20{+24}$ $4y = 4$ $\dfrac{4y}{{4}} = \dfrac{4}{{4}}$ ${y = 1}$ You can also plug ${x = 8}$ into $\thinspace {2x-3y = 13}\thinspace$ and get the same answer for $y$ : ${2}{(8)}{ - 3y = 13}$ ${y = 1}$